Two-dimensional Phase Gratings Research Articles

Dual-wavelength terahertz two-dimensional phase gratings based on all dielectric metasurfaces

Efficient and accurate phase gratings hold immense significance in the realization of large format heterodyne array receivers at terahertz frequencies. Metallic phase gratings have made substantial advancements in terms of operating wavelength and the number of diffraction beams. Like most other diffractive optical devices, metallic phase gratings are primarily optimized to operate at one specific wavelength. Metasurfaces compositing arrays of subwavelength nanostructures have been demonstrated with various optical functions, by freely modifying the polarization, phase, and amplitude of light. In this study, we present an approach to create a multi-wavelength phase grating compositing segments that incorporate multiple nanostructures. The resulting transmission phase grating not only exhibits uniform diffraction beams (2 × 2) but also achieves the same diffraction angles at both 1.31 and 2.7 THz. The measured total power efficiency of the diffraction beam pattern is 53.2% for 1.31 THz and 42.4% for 2.7 THz. These devices can be applied in terahertz astronomical observations and fluorescence microscopy applications, where multi-wavelength operation is necessary.

The U-Net-based phase-only CGH using the two-dimensional phase grating.

In this paper, the phase-only holograms with clear first diffraction orders have been generated based on the U-Net and the two-dimensional phase grating. Firstly, we proved the modulation effect of two-dimensional phase grating on diffraction field, and came to a conclusion that it could move the diffraction pattern of the hologram to the odd-numbered diffraction orders' center of that. Then we changed the generation process of phase-only holograms and the training strategy for U-Net according to this conclusion, which converted the optimization target of the U-Net from the zeroth diffraction order in the center of diffraction field to the first diffraction order in the edge of that. And we also used a method called "phase recombination" to improve the structure of U-Net for less memory footprint and faster generating speed. Finally, the holograms with the 4K resolution have been generated in 0.05s, and the average peak signal to noise ratio (PSNR) of the reconstructed images is about 37.2 dB in DIV2K-valid-HR dataset.

Development of terahertz two-dimensional phase gratings for multiple beam generation based on a high-accuracy phase retrieval algorithm.

High efficiency and accuracy phase gratings are of crucial importance for large format heterodyne array receivers at terahertz frequencies. Here, by developing a design approach that can create gratings with arbitrary two-dimensional diffraction distributions, we have realized a reflective metallic phase grating that generates 2×2 diffraction beams at 0.85 THz. The measured total power efficiency of the diffraction beam pattern is 81.9%, which demonstrates at least 17% improvement in efficiency compared with the standard pseudo-2D Fourier phase grating. In addition, we report the realization of up to 10×10 diffraction beam two-dimensional phase grating designs at terahertz wavelengths, using an adaptation of the Gerchberg-Saxton (GS) scheme known as the Mixed-Region-Amplitude-Freedom algorithm. Rigorous full wave simulation proves the efficiency and accuracy of the design, which overcomes the inaccurate intensity of the beam distribution drawbacks originated from the standard GS algorithm. The results pave the way for the development of large-pixel terahertz multi-beam heterodyne receivers.

Enhanced diffraction efficiency of two-dimensional phase gratings.

Phase gratings are used as beam multiplexers in the submillimeter and Terahertz spectral range. Two-dimensional beam arrangements can often be obtained most easily by the superposition of two one-dimensional grating structures. We show that in general this approach does not yield the maximum grating efficiency and propose a method to obtain significantly higher efficiencies for this grating class.

Optical encoder based on Fractional-Talbot effect using two-dimensional phase grating

This work presents an optical encoder that uses a two-dimensional phase grating. Rather than using a four-windowed scanning grating, this design with a special two-dimensional phase index grating generates two sinusoidal signals that are mutually phase-shifted by 180°. Afterwards, two large-areas, specially structured index grating generates the four 90° electrically phase-shifted scanning signals. The special design of the two-dimensional phase index grating provides more accuracy of phase-shift by using the fact that the + 1 and −1 diffraction orders are intrinsically phase-shifted from one another by 180°. The gap between the phase index grating and mail scale was increased to three quarters of Talbot distance. The tolerance of gap between the index and main grating is 0.1 mm. The tolerance of yaw motion is ± 0.25°.

The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays

The Talbot effect is the self-imaging, at distances D multiple of D(R), of the intensity downstream of a periodic object. Earlier work with hard synchrotron radiation X-rays showed the variation with D of the fundamental Fourier component of intensity to be a good measurement of beam coherence. Any higher-order Fourier coefficients I (D, m > 1) would be periodic with a reduced period D(Rm) = D(R)/m for an ideally coherent incident beam (partial Talbot effect). The degree of coherence gamma(x) is sampled through the ratio of I (D, m) at D = 0 and multiples of D(Rm). This requires the Fourier coefficient for D = 0, which is not accessible for a phase object (no contrast at D = 0). However, the ratio of the slopes of I (D, m) at D = 0 and D = pD(Rm) also provides this information. Furthermore, a characterization of gamma(x) is possible, provided an assumption is made on its shape, using only the ratio of the Fourier coefficient I (D, m) of two images a distance pD(Rm) apart. Experiments with one- and two-dimensional phase gratings and a mixed (amplitude and phase) two-dimensional grating confirm that the partial Talbot effect approach is viable. It requires a reduced range of distances, and yields important results directly, obviating the need for computer fits. In particular, 8% of the beam intensity was found to have very low coherence in the vertical direction, probably due to monochromator imperfection.

Multiple Imaging Using Various Types of Simple Phase Gratings

Diffraction gratings can be used to form multiple images in optical systems utilizing incoherent, monochromatic light. The properties of two-dimensional phase gratings having periodic rectangular, sinusoidal, or triangular surface corrugation have been investigated. It is shown that these gratings can be used to form an array of equally intense images by an optical cascading process, each step in the cascade increasing the number of images by a factor of 9. These simple gratings would be particularly useful for forming relatively small numbers of large images. The efficiency per step would be between 70% and 80% and the distortion less than 2%. If spatially incoherent laser light is used, the resolution and general image quality would be limited mainly by the lenses used. These conclusions are corroborated by experimental results obtained with rectangular-type phase gratings.

Fourier Images IV: The Phase Grating

The nature of the Fourier images obtained from phase objects is investigated theoretically both for the particular case of the sinusoidal grating and also for the general two-dimensional periodic object. The results are verified experimentally with light optics using a two-dimensional phase grating of 50 μ periodicity. A detailed investigation is made of the intensity distribution on planes mid-way between, and in the immediate neighbourhood of Fourier image planes. While there is no contrast on the Fourier image planes themselves, it is shown that a simple relationship (equation (3.4)) exists between the pattern on neighbouring planes and the phase distribution in the general two-dimensional object. It is shown that there will be no moire effect at full aperture for phase gratings effectively in contact. Analogies with the scattering of electrons by thin crystals are pointed out and it is indicated that under certain conditions a representation of the charge distribution will be obtained with modern electron microscopes. Full consideration of this point is deferred.